| Title:
|
Orthogonally additive functionals on $BV$ (English) |
| Author:
|
Khaing, Khaing Aye |
| Author:
|
Lee, Peng Yee |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
411-419 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we give a representation theorem for the orthogonally additive functionals on the space $BV$ in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type. (English) |
| Keyword:
|
functional |
| Keyword:
|
orthogonally additive functional |
| Keyword:
|
two-norm space |
| Keyword:
|
function of bounded variation |
| Keyword:
|
Henstock integral |
| Keyword:
|
Stieltjes integral |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| MSC:
|
26A45 |
| MSC:
|
46A70 |
| MSC:
|
46E99 |
| idZBL:
|
Zbl 1080.46506 |
| idMR:
|
MR2102614 |
| DOI:
|
10.21136/MB.2004.134042 |
| . |
| Date available:
|
2009-09-24T22:16:57Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134042 |
| . |
| Reference:
|
[1] J. Dieudonné: Foundations of Modern Analysis.Academic Press, N. Y., 1960. MR 0120319 |
| Reference:
|
[2] D. Franková: Regulated functions.Math. Bohem. 116 (1991), 20–59. MR 1100424 |
| Reference:
|
[3] T. H. Hildebrandt: Linear continuous functionals on the space $(BV)$ with weak topologies.Proc. Amer. Math. Soc. 17 (1966), 658–664. Zbl 0152.13604, MR 0193490 |
| Reference:
|
[4] P. Y. Lee: Lanzhou Lectures on Henstock Integration.World Scientific, 1989. Zbl 0699.26004, MR 1050957 |
| Reference:
|
[5] P. Y. Lee, R. Výborný: The Integral: An Easy Approach after Kurzweil and Henstock.Cambridge University Press, 2000. MR 1756319 |
| Reference:
|
[6] W. Orlicz: Linear Functional Analysis.World Scientific, 1992. Zbl 0799.46002, MR 1182560 |
| Reference:
|
[7] M. Tvrdý: Linear bounded functionals on the space of regular regulated functions.Tatra Mt. Math. Publ. 8 (1996), 203–210. MR 1475282 |
| Reference:
|
[8] A. Zygmund: Trigonometric Series I and II.Cambridge University Press, 1977. MR 0617944 |
| . |
